Question: Solve for $x$ and $y$ using elimination. ${-x+6y = 51}$ ${x-5y = -42}$
Explanation: We can eliminate $x$ by adding the equations together when the $x$ coefficients have opposite signs. Add the equations together. Notice that the terms $-x$ and $x$ cancel out. ${y = 9}$ Now that you know ${y = 9}$ , plug it back into $\thinspace {-x+6y = 51}\thinspace$ to find $x$ ${-x + 6}{(9)}{= 51}$ $-x+54 = 51$ $-x+54{-54} = 51{-54}$ $-x = -3$ $\dfrac{-x}{{-1}} = \dfrac{-3}{{-1}}$ ${x = 3}$ You can also plug ${y = 9}$ into $\thinspace {x-5y = -42}\thinspace$ and get the same answer for $x$ : ${x - 5}{(9)}{= -42}$ ${x = 3}$